Two-sample similarity test for the expected value of random intervals

Abstract

The similarity degree between the expectation of two random intervals is studied by means of a hypothesis testing procedure. For this purpose, a similarity measure for intervals is introduced based on the so-called Jaccard index for convex sets. The measure ranges from 0 (if both intervals are not similar at all, i.e., if they are not overlapped) to 1 (if both intervals are equal). A test statistic is proposed and its limit distribution is analyzed by considering asymptotic and bootstrap techniques. Some simulation studies are carried out to examine the behaviour of the approach.